On steady-state intercompartmental flows

The flow between compartments in physical and biological systems is treated as a special case of a more general theory of transitions between any two distinct sets A, Ā. Interest is focused on the flow rate from each set, i.e., the rate at which elements from that set appear in the other; and on the entry rate from each, i.e., the rate at which elements from the set leave to enter the region not part of either set. In particular, the two flow rates are completely determined by means of explicit expressions for their ratio (Theorem I) and difference (Theorem II) in terms of the two entry rates. An application to biological transport problems extends a result of Dantzig and Pace (1) by demonstrating that for a system of channels each narrow enough to effect a "lining-up" of particles, countergradient flows may result, i.e., flows for which the flow rate is greatest from the compartment with the smallest entry rate.